Incoming Senate Majority Leader Mitch McConnell, R-Ky., said his new goal for his Republican caucus is to not "scare" the American people.

"I don't want the American people to think that if they add a Republican president to a Republican Congress, that's going to be a scary outcome. I want the American people to be comfortable with the fact that the Republican House and Senate is a responsible, right-of-center, governing majority," McConnell told the Washington Post. "There would be nothing frightening about adding a Republican president to that governing majority... I think that's the single best thing we can do, is to not mess up the playing field, if you will, for whoever the nominee ultimately is."

When it comes to rank-and-file Republicans impulsively issuing threats that could stop the Senate in its tracks - like threatening amendments related to how Congress gets its health care - McConnell told the Post that he has already advised his members to "restrain themselves."

McConnell said the first real test could come by the end of this week in the form of an energy debate, and said he is trying to prevent his fellow Republicans from introducing amendments not related to energy issues.

The three issues McConnell believes have potential bipartisan common ground are international trade deals, an overhaul of the tax code and new revenue streams for infrastructure projects.

"Could the country use a lot more? You bet. But there's no way you can overcome a reluctant president on something really large," McConnell told the Post.

For the bigger issues, McConnell said he may have to force the president to use his veto pen, which would provide Republicans clear policy differentiations to campaign against in 2016.

In a Sunday interview with CNN, McConnell said he thinks the American people would like to see a "right-of-center, responsible conservative governing majority."

"That's what the speaker and I tend to provide. And, hopefully, we will have enough followers to do that."